There are an infinite number of possible word-to-world pairings in naturalistic learning environments. Previous studies to solve this mapping problem focus on linguistic, social, and representational constraints at a single moment. The proposed research asks if the indeterminacy problem may also be solved in another way, not in a single trial, but across trials, not in a single encounter with a word and potential referent but cross-situationally. We argue that a cross-situational learning strategy based on computing distributional statistics across words, across referents, and most importantly across the co-occurrences of these two can ultimately map individual words to the right referents despite the logical ambiguity in individual learning moments. Thus, the proposed research focuses on: (1) documenting cross-situational learning in infants from 10- to 16-months of age, (2) investigating the kinds of mechanisms that underlie this learning through both theoretical simulations and experimental studies, and (3) studying how statistical learning builds on itself accumulatively. Understanding those mechanisms and how they might go wrong or be bolstered are surely fundamental to understanding the origins of developmental language disorders that delay or alter early lexical learning. Implementing procedures to benefit children with developmental disorders typically involves altering or highlighting aspects of the learning environment. This requires a principled understanding of the structure and regularities of that environment and processes of statistical learning.